Since the conception of the AdS/CFT correspondence [1]}, [2]}, the scattering of particles and strings on AdS spaces has become an important subject of study, not only because it would improve our understanding on scattering amplitudes in curved space-times, but also because it will teach us about the large-\(N\)  expansion of conformal correlation functions in theories with holographic interpretation. On those theories, an expansion of a given correlation function in terms of \(1/N\)  should corresponds to an expansion in loops Witten diagrams in AdS gravity. Therefore, the development of techniques to compute loop Witten diagrams is imperative for the study of large \(N\)  conformal field theories. In addition, very recently [3]}, has been suggested that the on-shell kinematics of the flat-space S-matrix can be described by momentum diagrams in AdS, and in [4]} it was shown that indeed the factorization residues for the S-matrix in flat-space scalar theories might be described by Witten diagrams in AdS, implying that the perturbative flat-space S-matrix in \(d+2\)  dimensions might be related to correlation functions of some conformal field theory in \(d-\) dimension, which presents itself as a new interesting motivation to study Witten diagrams in AdS.
